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The three angles of a triangle are in the ratio 1 : 2 : 3. The sides opposite them are in the ratio:

Competition practiceTrigonometry
  • A1 : 2 : 3
  • B1 : √3 : 2
  • C1 : √2 : √3
  • D1 : √3 : 3

Step-by-Step Solution

The angles are 30°, 60° and 90°. By the sine rule the sides are proportional to the sines of their opposite angles: sin30° : sin60° : sin90° = 1/2 : √3/2 : 1 = 1 : √3 : 2. Sides grow with the sine of the angle, not with the angle itself, so 1 : 2 : 3 is the classic trap.
Answer: B) 1 : √3 : 2

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